The 4th Amendment is clear on warrants: "no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
The Constitution is utterly clear on warrants, and the law has been this way since 1789.
What the Americans of that era hated were general warrants that were issued (they were called "writs of assistance") which gave agents of the Crown the power to search for contraband without any limitation. With the 4th Amendment, they very sharply limited the circumstances under which a warrant could be issued, by whom, and for what purposes. They also put the asking for a warrant under the penalties of perjury, by requiring an oath to be sworn out.